It is known that particular compounds possess unique spectral signatures. One method to obtain a spectrum indicative of a particular compound is transmission spectroscopy. A transmission spectrum can be obtained by transmitting an energy beam of known intensity and frequency through an at least partially transmissive sample and recording the intensity of the energy transmitted through the sample at various incident wavelengths. This method works quite well for a wide range of compounds having known transmission spectra. More recent technology for obtaining infrared spectra uses interferometers and computers in what is commonly called Fourier Transform Infrared (FTIR) spectroscopy. This technology has proved to have significant advantages over prior art methods of obtaining infrared spectra. A transmission spectrum cannot, generally, be obtained for a compound composed of powder grains or small size granules, particularly when the powder is substantially opaque to the frequencies of the incident energy at common granule thickness. One solution in such an instance is to embed the powder or granules in a matrix not having spectral features in the frequency range of the incident energy beam. This method only works so long as a suitable matrix compound can be found and the powder or granules are not so opaque as to absorb all input energy when the matrix contains a sufficient density of the sample to produce a meaningful spectrum from the sample.
Another solution to the problem associated with powders or granular samples is to obtain a diffuse reflectance spectrum of the sample. A diffuse reflectance spectrum is obtained by directing an input energy beam onto the surface of the sample, collecting the diffusely reflected energy from the sample and directing that energy to a detector. Diffusely reflected energy is energy which is defined to be reflected from below the surface of the sample. The energy diffusely reflected from a sample does not have a preferred direction of reflection, i.e., the diffusely reflected energy leaves the sample surface in a hemispherical pattern. The diffusively reflected energy has spectral characteristics that uniquely identify the sample compounds and correspond to the spectrum obtained by transmissive means.
In addition to diffuse reflection, however, an energy beam directed against the surface of a sample produces specular reflection. Specular reflection is defined to be incident energy that is reflected from a surface of a sample as opposed to diffusely reflected energy which is energy reflected from below the sample surface. Specular reflectance obeys Snell's Law which states that the angle of incidence of the input energy beam equals the angle of reflectance. In other words, energy that is specularly reflected behaves as light reflected from a mirror. Thus, if all the crystals on the surface of a powder sample were oriented so as to present a homogenous reflective face to the incident energy that was parallel to the plane of the sample, the incident energy would reflect off the surface of the sample according to Snell's Law. However, the reflecting surfaces of individual crystals on the surface of a powder sample are somewhat randomly oriented and, therefore, scatter the incident energy over an entire hemisphere as is the case for diffuse reflection. Our experiments and those of others have shown that the crystals on the surface of a sample may often be oriented so as to produce a preferred direction of reflection. Nevertheless, some of the incident energy beam is nearly always specularly reflected over all angles of reflection. A detailed discussion of the spectrometry of powdered samples is found in Griffiths et al, Advance in Infrared and Raman Spectroscopy, Vol. 9, Chapter 2, (Heyden, London 1981) the disclosure of which is hereby incorporated by reference.
Conventional analysis of diffuse reflectance spectra employs the Kubelka-Munk function. The Kubelka-Munk function states that the strength of an absorption feature in a diffuse reflectance spectrum is linearly related to the concentration of the compound producing the spectral feature. The function involves a relationship between an absorption coefficient, a scattering coefficient and the ratio of the diffuse reflectance from a sample and that of a non-absorbing powder reference. The function assumes that the sample extends to an infinite optical depth, i.e., that depth at which the addition of more sample material to the bottom of the sample does not change the amount of energy diffusely reflected. In theory, the Kubelka-Munk function should enable a spectrum obtained by diffuse reflectance to be compared to a spectrum obtained by transmissive means. The transmission spectrum for many compounds is known. Hence, the ability to identify a compound from its diffuse reflectance spectrum given a known transmission spectrum enables diffuse reflectance spectroscopy to accurately identify trace elements present in powdered samples that do not lend themselves to direct transmission spectroscopy. A specific example of the application of diffuse reflection spectroscopy is in quality control of pharmaceutical tablets to eliminate the need to grind up the tablets and embed them in a non-absorbtive matrix. Moreover, it is believed that it will be possible to apply spectral subtraction routines commonly used in absorption spectroscopy to diffuse reflectance measurements to identify trace elements in the sample and to accurately establish their concentration in the sample.
The linearity of the Kubelka-Munk relationship for the strength of an absorption feature with concentration, however, breaks down for experimental conditions involving specular reflectance. Specular reflectance alters a diffuse spectrum in a complex manner which is not well understood. The spectrum produced from specular reflection is a complex, nonlinear function dependent on wavelength, particle size, index of refraction of the particular materials present in the sample, the presence or absence of an absorption band in the surface material and the strength of the band. Moreover, the spectrum obtained from a diffusely reflecting sample may change by simply changing the orientation of the sample or by merely brushing the surface of the sample. At best, specular reflectance convolves the Kubelka-Munk relationship with another slightly nonlinear function. In certain instances, such as for inorganic samples at infrared energies, the effect of specular reflectance is more severe, producing complete inversion of spectral bands, referred to as a reststrahlen bands, or derivative shaped spectral peaks. The effect of specular reflectance is to make quantitative analysis of the diffuse spectrum an extremely complicated and error prone undertaking. In many cases, qualitative interpretation of the diffuse reflectance spectrum convolved with specular reflection produces erroneous information as to the composition or concentration of a sample. Therefore, to obtain accurate and useful information, it is highly desirable to eliminate the specular reflectance component from the diffuse reflectance spectra.
As noted above, specular reflection behaves like a mirror with incident energy reflected from a powder surface according to Snell's Law without penetrating into the sample. Any specular component should ideally leave the sample with a smaller angular spread than the diffuse component. Although powdered or granular surfaces adhere to Snell's Law for individual granules, the reflection properties of the aggregate surface can be quite different. However, surface preparation techniques could be used to orient the surface granules so that Snell's Law reasonably approximates the reflectance off the surface. Therefore, certain collection angles could, in principle, contain a pure diffuse reflection spectrum, and rotation of the collection mirror away from a symmetrical collection angle would eliminate the specular component of the energy reflected back from the sample.
Our experiments have shown that specular reflection may indeed have a preferential orientation along the direction predicated by Snell's Law. However, some specularly reflected energy has been found at all angles of reflection. The magnitude of the specular component over a given angle is a function of the manner in which the sample cup is filled and prepared. Standard practice in examining a powder sample has included drawing a straight edge across the powder surface prior to taking a spectrum. This manner of preparing the surface appears to be highly effective at orienting individual crystals and increases the likelihood that a comparable diffuse reflectance spectrum may be obtained from samples that are identical in composition. However, orienting the surface crystals increases the magnitude of energy that is specularly reflected towards the detector without confining the specular reflection to a particular angle. Thus, while this method might improve repeatability inherent distortions are also repeated.
Roughening the surface of the sample reduces the total amount of specular reflectance directed towards the collector. The roughening may take the form of drawing a camel hair brush over the sample or placing a piece of adhesive tape in light contact with the top of the sample and subsequently removing the tape. However, roughening the surface to the same degree is difficult and does not completely eliminate the specular component. Indeed, a completely roughened surface having crystals randomly oriented produces specular reflection over all angles of reflection without a known preferred orientation.
Another method of attempting to eliminate the specular component from a diffuse reflectance spectrum involves diluting the specularly reflective sample in a matrix having no spectral features a the wavelength of the incident energy and no distorted specular reflectance properties. This method is subject to the limitation of being able to find an inert matrix material that does not have absorptive or reflective properties in the given range of energy. The method often requires destroying the sample so that it can be mixed with the matrix material.
The foregoing discussion demonstrates an acknowledged need for some means by which to eliminate specular reflection from diffuse reflectance spectra. We have found a particular need for eliminating the distortion caused by specular reflectance in obtaining diffuse reflectance spectra of inorganic compounds. This is because certain inorganic compounds are not suited for infrared analysis by transmssive means and may not be analyzed with any of the foregoing methods due to the extreme distortion of their diffuse reflectance spectrum caused by their inherent specular properties. More generally, there has not hitherto been a simple means for quickly and economically obtaining an undistorted diffuse reflectance spectrum of any sample having specular reflective properties that is not subject to random distortions caused by the orientation of granules on the surface of the sample.